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Re: Finding Roots of Polynomials over Polynomial Quotient Rings

• To: mathgroup at smc.vnet.net
• Subject: [mg93469] Re: [mg93457] Finding Roots of Polynomials over Polynomial Quotient Rings
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 10 Nov 2008 03:30:12 -0500 (EST)
• References: <200811091025.FAA20508@smc.vnet.net>

On 9 Nov 2008, at 19:25, Julian wrote:

> Hi all,
>
> Just wondering how I would go about finding roots of an polynomial,
> say t^2 +2, over a quotient ring, say Z/5Z[x] / <x^2+2>, in
> Mathematica?  The modulus option in Reduce is only for integers, and
> I've had trouble finding anything relevant in the finite fields
> package... anyone know if this can be done in Mathematica?
>
> Thanks,
> Julian
>

Since a finite field has only finitely many elements and since the  
FiniteFields package lets you perform arithmetic on these elements,  
you can always find the roots of a polynomial simply by substituting  
all the field elements into the polynomial and selecting those that  
satisfy it. Or am I misunderstanding your question?

Andrzej Kozlowski

• References:
  • Finding Roots of Polynomials over Polynomial Quotient Rings
    • From: Julian <julianhaw@gmail.com>